A train passes through a station with a constant speed. A stationary observer at the station platform measures the tone of the train whistle as $$484$$ Hz when it approaches the station and $$442$$ Hz when it leaves the station. If the sound velocity in air is $$330m/s$$, then the tone of the whistle and the speed of the train are

Question

A train passes through a station with a constant speed. A stationary observer at the station platform measures the tone of the train whistle as $$484$$ Hz when it approaches the station and  $$442$$ Hz when it leaves the station. If the sound velocity in air is  $$330m/s$$, then the tone of the whistle and the speed of the train are

Infinity Learn · Accepted Answer

When train approaches the station, the frequency heard by the observerυ$$1=$$υvv−$$vs=$$υ$$330330$$−vsHere,  $$v=330$$ $$m/s$$υ is the actual frequency of the $$whistle484=$$υ$$330330$$−vs....$$.1When$$ the train leaves the stationυ$$2=$$υ$$vv+vs=$$υ$$330330+vs$$...$$.2Divide$$ Equations (1) & (2), we get⇒$$484442=330+vs330$$−vs⇒$$1.09=330+vs330$$−vs⇒$$vs=31.352.09=15$$ $$m/s=15$$ ×$$185=54kmphSubstituting$$  vs in equation gives⇒$$484=$$υ$$330330$$−$$15=$$υ$$330315$$⇒υ$$=484$$×$$2122$$∴υ$$=462$$ HzTherefore, the correct answer is (A).

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